Classification using graph partitioning

This paper explores the classification problem based on parallel feature partitioning. This formulation leads to a new problem in computational geometry. While this new problem appears to be NP-complete, it is shown that the proposed graph theoretical platform makes it semi-tractable, allowing the use of conventional tools for its solution. Here, by conventional, we mean any exact or heuristic algorithm for partitioning a graph into a minimal number of cliques or for finding the clique of maximum cardinality while seeking an efficient heuristic algorithm. An important advantage of this approach is the decomposition of a problem involving l classes into l optimization problems involving a single class. The computational complexity of the method, computational procedures, and classification rules are discussed. A geometrical interpretation of the solution is also given. Using the proposed approach, the geometrical structure of the training set is utilized in the best possible way.